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1. In the next World cup of cricket there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. Four top teams of this round will qualify for the semifinal round, where they play the best of three matches. The Minimum number of matches in the next World cup will be:

Solution:
The number of matches in first round,
= 6C2 +6C2
Number of matches in next round,
= 6C2
Number of matches in semifinals,
= 4C2
Total number of matches,
= 6C2 + 6C2 + 6C2 + 4C2 + 2
= 53

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